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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Random Riesz energies on compact Kähler manifolds


Authors: Renjie Feng and Steve Zelditch
Journal: Trans. Amer. Math. Soc. 365 (2013), 5579-5604
MSC (2010): Primary 58J37, 32L81, 32A60, 60D05
Published electronically: March 12, 2013
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Abstract: The expected Riesz energies $ E_{\mu ^N_h}\mathcal E_{s}$ of the zero sets of systems of independent Gaussian random polynomials of degree $ N$ are determined asymptotically as the degree $ N \to \infty $ in all dimensions and codimensions. The asymptotics are proved for sections of any positive line bundle over any compact Kähler manifold.


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Additional Information

Renjie Feng
Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 0G4
Email: renjie@math.mcgill.ca

Steve Zelditch
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: zelditch@math.northwestern.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05870-9
PII: S 0002-9947(2013)05870-9
Received by editor(s): January 11, 2012
Received by editor(s) in revised form: April 23, 2012
Published electronically: March 12, 2013
Additional Notes: This research was partially supported by NSF grant #DMS-0904252.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.